The University of Michigan Combinatorics Seminar


Abstract 

Spaces with convex ear decompositions were introduced by
Chari. A simplicial complex has a convex ear decomposition if it can
be built by starting with the boundary of a convex polytope, and then
attaching balls of the same dimension which are subcomplexes of
(possibly other) convex polytopes. Examples include matroid
complexes, order complexes of geometric lattices and spherical
buildings. The hvectors of these spaces satisfy a number of
inequalities similar to those suggested by the gtheorem for convex
polytopes. These inequalities lead to a number of interesting
combinatorial problems.
